What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
8001 | (2^346318+862)/2 | 104252 | Stefano Morozzi | 02/2021 |
8009 | 18^83049-89 | 104250 | Lelio R Paula | 01/2017 |
8008 | (2^346311+606)/2 | 104250 | Stefano Morozzi | 09/2020 |
8002 | 2^346308+92347 | 104250 | Stefano Morozzi | 11/2024 |
8003 | 2^346308+182521 | 104250 | Stefano Morozzi | 11/2024 |
8004 | 2^346309+128897 | 104250 | Stefano Morozzi | 11/2024 |
8005 | 2^346309+184955 | 104250 | Stefano Morozzi | 11/2024 |
8006 | 2^346310+303 | 104250 | Stefano Morozzi | 11/2024 |
8007 | 2^346311+32693 | 104250 | Stefano Morozzi | 11/2024 |
8010 | 2^346305+165741 | 104249 | Stefano Morozzi | 11/2024 |
8011 | 2^346302+75075 | 104248 | Stefano Morozzi | 11/2024 |
8012 | 2^346304+33411 | 104248 | Stefano Morozzi | 11/2024 |
8013 | 2^346298+147849 | 104247 | Stefano Morozzi | 11/2024 |
8014 | 2^346300+144855 | 104247 | Stefano Morozzi | 11/2024 |
8015 | 2^346296+44865 | 104246 | Stefano Morozzi | 11/2024 |
8016 | 2^346297+116291 | 104246 | Stefano Morozzi | 11/2024 |
8017 | 2^346297+142667 | 104246 | Stefano Morozzi | 11/2024 |
8018 | 2^346293+39285 | 104245 | Stefano Morozzi | 11/2024 |
8019 | 2^346293+58929 | 104245 | Stefano Morozzi | 11/2024 |
8020 | 2^346294+151075 | 104245 | Stefano Morozzi | 11/2024 |
8021 | 2^346290+162153 | 104244 | Stefano Morozzi | 11/2024 |
8022 | 2^346286+139935 | 104243 | Stefano Morozzi | 11/2024 |
8023 | 2^346282+184705 | 104242 | Stefano Morozzi | 11/2024 |
8024 | 2^346283+116913 | 104242 | Stefano Morozzi | 11/2024 |
8025 | 2^346284+118191 | 104242 | Stefano Morozzi | 11/2024 |
8026 | 2^346284+186595 | 104242 | Stefano Morozzi | 11/2024 |
8027 | 2^346279+29591 | 104241 | Stefano Morozzi | 11/2024 |
8028 | 2^346279+122385 | 104241 | Stefano Morozzi | 11/2024 |
8029 | 2^346280+18925 | 104241 | Stefano Morozzi | 11/2024 |
8030 | 2^346281+69725 | 104241 | Stefano Morozzi | 11/2024 |
8031 | 2^346281+156401 | 104241 | Stefano Morozzi | 11/2024 |
8032 | 2^346275+182519 | 104240 | Stefano Morozzi | 11/2024 |
8033 | 2^346276+14101 | 104240 | Stefano Morozzi | 11/2024 |
8034 | 2^346276+189937 | 104240 | Stefano Morozzi | 11/2024 |
8035 | 2^346273+121425 | 104239 | Stefano Morozzi | 11/2024 |
8036 | 2^346274+72363 | 104239 | Stefano Morozzi | 11/2024 |
8037 | 2^346274+92047 | 104239 | Stefano Morozzi | 11/2024 |
8038 | 2^346268+44233 | 104238 | Stefano Morozzi | 11/2024 |
8039 | 2^346270+19539 | 104238 | Stefano Morozzi | 11/2024 |
8040 | 2^346265+133877 | 104237 | Stefano Morozzi | 11/2024 |
8041 | 2^346267+64613 | 104237 | Stefano Morozzi | 11/2024 |
8042 | 2^346267+70461 | 104237 | Stefano Morozzi | 11/2024 |
8043 | 2^346267+118715 | 104237 | Stefano Morozzi | 11/2024 |
8044 | 2^346263+110721 | 104236 | Stefano Morozzi | 11/2024 |
8045 | 2^346263+165009 | 104236 | Stefano Morozzi | 11/2024 |
8046 | 2^346264+50481 | 104236 | Stefano Morozzi | 11/2024 |
8047 | 2^346264+134047 | 104236 | Stefano Morozzi | 11/2024 |
8048 | 2^346264+179617 | 104236 | Stefano Morozzi | 11/2024 |
8049 | 2^346260+176391 | 104235 | Stefano Morozzi | 11/2024 |
8050 | 2^346256+36111 | 104234 | Stefano Morozzi | 11/2024 |
8051 | 2^346254+52299 | 104233 | Stefano Morozzi | 11/2024 |
8057 | (166*10^104230+11)/3 | 104232 | Robert Price | 03/2021 |
8052 | 2^346248+3075 | 104232 | Stefano Morozzi | 11/2024 |
8053 | 2^346248+39081 | 104232 | Stefano Morozzi | 11/2024 |
8054 | 2^346249+38339 | 104232 | Stefano Morozzi | 11/2024 |
8055 | 2^346251+32831 | 104232 | Stefano Morozzi | 11/2024 |
8056 | 2^346251+116175 | 104232 | Stefano Morozzi | 11/2024 |
8058 | 2^346247+197309 | 104231 | Stefano Morozzi | 11/2024 |
8059 | 2^346245+95429 | 104231 | Stefano Morozzi | 11/2024 |
8060 | 2^346243+58163 | 104230 | Stefano Morozzi | 11/2024 |
8061 | 2^346243+130931 | 104230 | Stefano Morozzi | 11/2024 |
8062 | 2^346244+10381 | 104230 | Stefano Morozzi | 11/2024 |
8063 | 2^346241+41057 | 104229 | Stefano Morozzi | 11/2024 |
8064 | 2^346235+152303 | 104228 | Stefano Morozzi | 11/2024 |
8065 | 2^346236+106617 | 104228 | Stefano Morozzi | 11/2024 |
8066 | 2^346232+103317 | 104227 | Stefano Morozzi | 11/2024 |
8067 | 2^346232+193681 | 104227 | Stefano Morozzi | 11/2024 |
8068 | 2^346233+115671 | 104227 | Stefano Morozzi | 11/2024 |
8069 | 2^346229+73157 | 104226 | Stefano Morozzi | 11/2024 |
8070 | 2^346229+145377 | 104226 | Stefano Morozzi | 11/2024 |
8071 | 2^346230+171103 | 104226 | Stefano Morozzi | 11/2024 |
8072 | 2^346225+55527 | 104225 | Stefano Morozzi | 11/2024 |
8073 | 2^346225+132251 | 104225 | Stefano Morozzi | 11/2024 |
8074 | 2^346225+140637 | 104225 | Stefano Morozzi | 11/2024 |
8075 | 2^346223+27335 | 104224 | Stefano Morozzi | 11/2024 |
8076 | 2^346223+74591 | 104224 | Stefano Morozzi | 11/2024 |
8077 | 2^346224+70905 | 104224 | Stefano Morozzi | 11/2024 |
8078 | 2^346220+12355 | 104223 | Stefano Morozzi | 11/2024 |
8079 | 2^346220+110805 | 104223 | Stefano Morozzi | 11/2024 |
8080 | 2^346220+161361 | 104223 | Stefano Morozzi | 11/2024 |
8081 | 2^346220+176523 | 104223 | Stefano Morozzi | 11/2024 |
8082 | 2^346220+185625 | 104223 | Stefano Morozzi | 11/2024 |
8083 | 2^346216+62973 | 104222 | Stefano Morozzi | 11/2024 |
8084 | 2^346217+88391 | 104222 | Stefano Morozzi | 11/2024 |
8085 | 2^346217+170121 | 104222 | Stefano Morozzi | 11/2024 |
8086 | 2^346217+111567 | 104222 | Stefano Morozzi | 11/2024 |
8090 | 2^346213+484049 | 104221 | Enzo Doria | 04/2017 |
8087 | 2^346212+31773 | 104221 | Stefano Morozzi | 11/2024 |
8088 | 2^346213+37151 | 104221 | Stefano Morozzi | 11/2024 |
8089 | 2^346213+162399 | 104221 | Stefano Morozzi | 11/2024 |
8091 | 2^346209+173231 | 104220 | Stefano Morozzi | 11/2024 |
8092 | 2^346207+125243 | 104219 | Stefano Morozzi | 11/2024 |
8093 | 2^346208+79825 | 104219 | Stefano Morozzi | 11/2024 |
8094 | 2^346208+176463 | 104219 | Stefano Morozzi | 11/2024 |
8095 | 2^346206+195363 | 104219 | Stefano Morozzi | 11/2024 |
8096 | 2^346202+67065 | 104218 | Stefano Morozzi | 11/2024 |
8097 | 2^346202+107377 | 104218 | Stefano Morozzi | 11/2024 |
8098 | 2^346204+127677 | 104218 | Stefano Morozzi | 11/2024 |
8099 | 2^346204+19573 | 104218 | Stefano Morozzi | 11/2024 |
8100 | 2^346204+161997 | 104218 | Stefano Morozzi | 11/2024 |
8101 | 2^346204+152665 | 104218 | Stefano Morozzi | 11/2024 |
8102 | 2^346199+90995 | 104217 | Stefano Morozzi | 11/2024 |
8103 | 2^346199+189629 | 104217 | Stefano Morozzi | 11/2024 |
8104 | 2^346200+159591 | 104217 | Stefano Morozzi | 11/2024 |
8105 | 2^346195+19733 | 104216 | Stefano Morozzi | 11/2024 |
8106 | 2^346196+141117 | 104216 | Stefano Morozzi | 11/2024 |
8107 | 2^346196+195171 | 104216 | Stefano Morozzi | 11/2024 |
8108 | 2^346197+113751 | 104216 | Stefano Morozzi | 11/2024 |
8109 | 2^346198+95305 | 104216 | Stefano Morozzi | 11/2024 |
8110 | 2^346198+106735 | 104216 | Stefano Morozzi | 11/2024 |
8112 | 18^83021-91 | 104214 | Lelio R Paula | 01/2017 |
8111 | 2^346189+194831 | 104214 | Stefano Morozzi | 11/2024 |
8113 | 10^104212+128779 | 104213 | Patrick De Geest | 05/2016 |
8114 | 10^104212+237447 | 104213 | Patrick De Geest | 05/2016 |
8115 | 10^104212+242139 | 104213 | Patrick De Geest | 05/2016 |
8116 | 10^104212+269199 | 104213 | Patrick De Geest | 05/2016 |
8120 | 24254^19803+19803^24254 | 104213 | Hans Havermann | 09/2020 |
8117 | 2^346186+93813 | 104213 | Stefano Morozzi | 11/2024 |
8118 | 2^346186+153687 | 104213 | Stefano Morozzi | 11/2024 |
8119 | 2^346187+102195 | 104213 | Stefano Morozzi | 11/2024 |
8125 | (10^104212-71)/1 | 104212 | Serge Batalov | 12/2014 |
8121 | 2^346182+118065 | 104212 | Stefano Morozzi | 11/2024 |
8122 | 2^346184+155085 | 104212 | Stefano Morozzi | 11/2024 |
8123 | 2^346184+187513 | 104212 | Stefano Morozzi | 11/2024 |
8124 | 2^346184+188455 | 104212 | Stefano Morozzi | 11/2024 |
8126 | 2^346180+82735 | 104211 | Stefano Morozzi | 11/2024 |
8127 | 2^346180+160593 | 104211 | Stefano Morozzi | 11/2024 |
8128 | 2^346180+192333 | 104211 | Stefano Morozzi | 11/2024 |
8129 | 2^346181+199821 | 104211 | Stefano Morozzi | 11/2024 |
8130 | 2^346176+123667 | 104210 | Stefano Morozzi | 11/2024 |
8131 | 2^346178+37455 | 104210 | Stefano Morozzi | 11/2024 |
8132 | 2^346178+95865 | 104210 | Stefano Morozzi | 11/2024 |
8133 | 2^346178+159517 | 104210 | Stefano Morozzi | 11/2024 |
8134 | 2^346174+12543 | 104209 | Stefano Morozzi | 11/2024 |
8135 | 2^346169+56049 | 104208 | Stefano Morozzi | 11/2024 |
8136 | 2^346169+118965 | 104208 | Stefano Morozzi | 11/2024 |
8137 | 2^346170+31363 | 104208 | Stefano Morozzi | 11/2024 |
8138 | 2^346165+61767 | 104207 | Stefano Morozzi | 11/2024 |
8139 | 2^346166+189919 | 104207 | Stefano Morozzi | 11/2024 |
8140 | 2^346167+41681 | 104207 | Stefano Morozzi | 11/2024 |
8141 | 2^346162+85765 | 104206 | Stefano Morozzi | 11/2024 |
8142 | 2^346164+152925 | 104206 | Stefano Morozzi | 11/2024 |
8143 | 2^346160+131703 | 104205 | Stefano Morozzi | 11/2024 |
8144 | 2^346155+166433 | 104204 | Stefano Morozzi | 11/2024 |
8145 | 2^346157+7137 | 104204 | Stefano Morozzi | 11/2024 |
8146 | 2^346158+31483 | 104204 | Stefano Morozzi | 11/2024 |
8147 | 2^346158+183253 | 104204 | Stefano Morozzi | 11/2024 |
8148 | 2^346152+136287 | 104203 | Stefano Morozzi | 11/2024 |
8149 | 2^346154+107499 | 104203 | Stefano Morozzi | 11/2024 |
8150 | 2^346154+187987 | 104203 | Stefano Morozzi | 11/2024 |
8154 | 23678^23821-23821^23678 | 104202 | Norbert Schneider | 01/2020 |
8151 | 2^346149+45857 | 104202 | Stefano Morozzi | 11/2024 |
8152 | 2^346150+111579 | 104202 | Stefano Morozzi | 11/2024 |
8153 | 2^346151+21539 | 104202 | Stefano Morozzi | 11/2024 |
8155 | 2^346143+119183 | 104200 | Stefano Morozzi | 11/2024 |
8156 | 2^346143+130361 | 104200 | Stefano Morozzi | 11/2024 |
8157 | 2^346143+171791 | 104200 | Stefano Morozzi | 11/2024 |
8158 | 2^346144+4731 | 104200 | Stefano Morozzi | 11/2024 |
8159 | 2^346144+158097 | 104200 | Stefano Morozzi | 11/2024 |
8160 | 2^346139+68459 | 104199 | Stefano Morozzi | 11/2024 |
8161 | 2^346140+121711 | 104199 | Stefano Morozzi | 11/2024 |
8162 | 2^346135+122913 | 104198 | Stefano Morozzi | 11/2024 |
8163 | 2^346135+125453 | 104198 | Stefano Morozzi | 11/2024 |
8164 | 2^346135+184869 | 104198 | Stefano Morozzi | 11/2024 |
8165 | 2^346136+135721 | 104198 | Stefano Morozzi | 11/2024 |
8166 | 2^346133+46695 | 104197 | Stefano Morozzi | 11/2024 |
8167 | 2^346129+87819 | 104196 | Stefano Morozzi | 11/2024 |
8168 | 2^346130+127369 | 104196 | Stefano Morozzi | 11/2024 |
8169 | 2^346130+177619 | 104196 | Stefano Morozzi | 11/2024 |
8170 | 2^346125+105609 | 104195 | Stefano Morozzi | 11/2024 |
8171 | 2^346127+71201 | 104195 | Stefano Morozzi | 11/2024 |
8172 | 2^346122+74469 | 104194 | Stefano Morozzi | 11/2024 |
8173 | 2^346122+124119 | 104194 | Stefano Morozzi | 11/2024 |
8174 | 2^346122+124227 | 104194 | Stefano Morozzi | 11/2024 |
8175 | 2^346124+83973 | 104194 | Stefano Morozzi | 11/2024 |
8176 | 2^346124+186877 | 104194 | Stefano Morozzi | 11/2024 |
8177 | 2^346121+174729 | 104193 | Stefano Morozzi | 11/2024 |
8178 | 2^346116+166317 | 104192 | Stefano Morozzi | 11/2024 |
8179 | 2^346117+98015 | 104192 | Stefano Morozzi | 11/2024 |
8180 | (13*31^69863+12407)/30 | 104191 | Eric Chen | 04/2024 |
8181 | 2^346112+20827 | 104191 | Stefano Morozzi | 11/2024 |
8182 | 2^346112+77533 | 104191 | Stefano Morozzi | 11/2024 |
8183 | 2^346114+76959 | 104191 | Stefano Morozzi | 11/2024 |
8184 | 2^346115+30513 | 104191 | Stefano Morozzi | 11/2024 |
8185 | 2^346115+90105 | 104191 | Stefano Morozzi | 11/2024 |
8186 | 2^346115+155859 | 104191 | Stefano Morozzi | 11/2024 |
8187 | 2^346115+157809 | 104191 | Stefano Morozzi | 11/2024 |
8188 | 2^346109+118587 | 104190 | Stefano Morozzi | 11/2024 |
8189 | 2^346110+105763 | 104190 | Stefano Morozzi | 11/2024 |
8190 | 2^346110+175197 | 104190 | Stefano Morozzi | 11/2024 |
8191 | 2^346110+197725 | 104190 | Stefano Morozzi | 11/2024 |
8192 | 2^346111+143313 | 104190 | Stefano Morozzi | 11/2024 |
8193 | 2^346107+153513 | 104189 | Stefano Morozzi | 11/2024 |
8194 | 2^346108+153897 | 104189 | Stefano Morozzi | 11/2024 |
8195 | 2^346102+79435 | 104188 | Stefano Morozzi | 11/2024 |
8196 | 2^346102+131949 | 104188 | Stefano Morozzi | 11/2024 |
8197 | 2^346103+123009 | 104188 | Stefano Morozzi | 11/2024 |
8198 | 2^346104+115845 | 104188 | Stefano Morozzi | 11/2024 |
8199 | 2^346105+29141 | 104188 | Stefano Morozzi | 11/2024 |
8200 | 2^346105+85035 | 104188 | Stefano Morozzi | 11/2024 |
8201 | 2^346098+80323 | 104186 | Stefano Morozzi | 11/2024 |
8202 | 2^346092+69855 | 104185 | Stefano Morozzi | 11/2024 |
8203 | 2^346093+3627 | 104185 | Stefano Morozzi | 11/2024 |
8204 | 2^346089+90947 | 104184 | Stefano Morozzi | 11/2024 |
8205 | 2^346089+186749 | 104184 | Stefano Morozzi | 11/2024 |
8206 | 2^346091+71279 | 104184 | Stefano Morozzi | 11/2024 |
8207 | 2^346084+69211 | 104182 | Stefano Morozzi | 11/2024 |
8208 | 2^346084+112237 | 104182 | Stefano Morozzi | 11/2024 |
8209 | 2^346079+10371 | 104181 | Stefano Morozzi | 11/2024 |
8210 | 2^346079+82811 | 104181 | Stefano Morozzi | 11/2024 |
8214 | 2^346078+7695 | 104180 | Lelio R Paula | 12/2016 |
8211 | 2^346076+85903 | 104180 | Stefano Morozzi | 11/2024 |
8212 | 2^346076+111577 | 104180 | Stefano Morozzi | 11/2024 |
8213 | 2^346076+143047 | 104180 | Stefano Morozzi | 11/2024 |
8215 | 2^346072+126673 | 104179 | Stefano Morozzi | 11/2024 |
8216 | 2^346073+37899 | 104179 | Stefano Morozzi | 11/2024 |
8217 | 2^346075+21519 | 104179 | Stefano Morozzi | 11/2024 |
8218 | 2^346075+27255 | 104179 | Stefano Morozzi | 11/2024 |
8219 | 2^346075+115331 | 104179 | Stefano Morozzi | 11/2024 |
8220 | 2^346069+53615 | 104178 | Stefano Morozzi | 11/2024 |
8221 | 2^346069+188087 | 104178 | Stefano Morozzi | 11/2024 |
8222 | 2^346066+29949 | 104177 | Stefano Morozzi | 11/2024 |
8223 | 2^346066+133909 | 104177 | Stefano Morozzi | 11/2024 |
8224 | 2^346066+188535 | 104177 | Stefano Morozzi | 11/2024 |
8225 | 2^346068+159553 | 104177 | Stefano Morozzi | 11/2024 |
8226 | 2^346064+122683 | 104176 | Stefano Morozzi | 11/2024 |
8227 | 2^346060+20325 | 104175 | Stefano Morozzi | 11/2024 |
8228 | 2^346060+110755 | 104175 | Stefano Morozzi | 11/2024 |
8229 | 2^346058+57933 | 104174 | Stefano Morozzi | 11/2024 |
8235 | 2^346055-19537 | 104173 | Enzo Doria | 05/2013 |
8236 | (3*2^346057+1)/77 | 104173 | Lelio R Paula | 12/2013 |
8230 | 2^346052+26655 | 104173 | Stefano Morozzi | 11/2024 |
8231 | 2^346052+31611 | 104173 | Stefano Morozzi | 11/2024 |
8232 | 2^346053+67667 | 104173 | Stefano Morozzi | 11/2024 |
8233 | 2^346054+30507 | 104173 | Stefano Morozzi | 11/2024 |
8234 | 2^346054+194589 | 104173 | Stefano Morozzi | 11/2024 |
8237 | 2^346049+59067 | 104172 | Stefano Morozzi | 11/2024 |
8238 | 2^346050+3129 | 104172 | Stefano Morozzi | 11/2024 |
8239 | 2^346050+167125 | 104172 | Stefano Morozzi | 11/2024 |
8240 | 2^346051+52563 | 104172 | Stefano Morozzi | 11/2024 |
8241 | 2^346051+90941 | 104172 | Stefano Morozzi | 11/2024 |
8242 | 2^346046+172107 | 104171 | Stefano Morozzi | 11/2024 |
8243 | 2^346048+63415 | 104171 | Stefano Morozzi | 11/2024 |
8244 | 2^346041+197885 | 104169 | Stefano Morozzi | 11/2024 |
8248 | 2^346037-20125 | 104168 | Enzo Doria | 06/2013 |
8245 | 2^346036+80773 | 104168 | Stefano Morozzi | 11/2024 |
8246 | 2^346037+116429 | 104168 | Stefano Morozzi | 11/2024 |
8247 | 2^346038+147549 | 104168 | Stefano Morozzi | 11/2024 |
8249 | 2^346034+2205 | 104167 | Stefano Morozzi | 11/2024 |
8250 | 2^346031+56429 | 104166 | Stefano Morozzi | 11/2024 |